Yes, I should have used the term 'cheer for' or 'support' instead of 'vote for' as I guess it was a lame word to use. My bad. Hey, don't apologize for the length of your post as it makes for an interesting read.
In regard to the size of Montreal compared to Winnipeg you are indeed correct in pointing out how much larger Montreal is. However, in relation to the population of each city to that of the rest of the province, Winnipeg (61%) represents a higher percentage compared to Montreal (49%). The situation with Saskatchewan is much different in that you have 2 cities (Regina and Saskatoon) which are relatively equal in population and neither one has a higher percentage living there than in the rest of the province. If the team were to be called Regina Roughriders it may cause some jealousy in Saskatoon. However, the capital region of Winnipeg has a population of 811,874 while Manitoba has an overall population of 1,328,346 (2017 Q1).
I know you are making the point based on the CFL but suggesting the Bombers may draw more fans simply by having the name Manitoba instead of Winnipeg doesn't convince me that it would occur. The Roughriders draw more fans to their games than the Argos do in Canada's largest city. It's clear the Riders have the best fan base in the league. The Bombers draw relatively well in comparison to other CFL teams but they are not the only game in town. Not only do they have to deal with a fan base that can be fickle when they're not winning but also with our city being in such close proximity to the lakes and cottage country with a short summer. There's also the competition for dollars with the Winnipeg Jets, Manitoba Moose and Winnipeg Goldeyes. Then there's also the Arts which includes the Winnipeg Symphony Orchestra and Royal Winnipeg Ballet. There are so many options available that it will always be a challenge for the Bombers. However, in spite of all that, the Bombers are relatively successful and have good support. I just don't think someone's going to come down to Winnipeg from Thompson or Flin Flon to watch the Bombers simply because they're called Manitoba. The fans will come because they like football or the team is winning.
Let us remember that the Blue Jays have fans across the country even though they are based in Toronto. They don't have to be called the Ontario Blue Jays for the rest of the province to support them or the Canada Blue Jays for the rest of the country to cheer for them. Wherever possible it makes sense to use the name of the city where a team is based as it provides more of a focal point for people in general in visualizing where the team plays its home games and where they're from when on the road. In some situations where there are 2 cities of relatively equal size in a particular province or state it may be the right choice to use the province or state name for the team but otherwise I always prefer the name of the city for the team.